Question

В колхоз входят жители трёх соседних сёл. Число семей первого села составляет 3/10 всех семей колхоза; во втором селе число семей в 11/2 раза больше, чем в первом, а в третьем селе число семей на 420 меньше, чем во втором. Сколько всего семей в колхозе?

Answer 1

Пусть в колхозе х семей, тогда в первом селе 3/10х, тогда во втором колхозе 3/10*3/2х, а в третьем селе 3/10*3/2х-420.
3/10*3/2х+3/10*3/2х-420+3/10х=х
9/20х+9/20х-420+3/10х=х
18/20х+3/10х-420=х
9/10х+3/10х-х=420
12/10х-х=420
2/10х=420
х=420*10:2
х=2100 семей в колхозе

Answer 2

Calculation of the Total Number of Families in the Collective Farm

To calculate the total number of families in the collective farm, we need to consider the information provided about the three neighboring villages.

Let's break down the information given:

- The number of families in the first village is 3/10 of all the families in the collective farm. - The number of families in the second village is 11/2 times greater than the number in the first village. - The number of families in the third village is 420 less than the number in the second village.

To find the total number of families in the collective farm, we'll follow these steps:

1. Let's assume the total number of families in the collective farm is represented by the variable x. 2. The number of families in the first village is 3/10 of x, which can be expressed as (3/10)x. 3. The number of families in the second village is 11/2 times greater than the number in the first village, so it can be expressed as (11/2)(3/10)x. 4. The number of families in the third village is 420 less than the number in the second village, so it can be expressed as [(11/2)(3/10)x] - 420.

Now, we can set up an equation to find the value of x:

[(11/2)(3/10)x] - 420 = x

To solve this equation, we can simplify it:

[(33/20)x] - 420 = x

Next, we'll isolate x on one side of the equation:

[(33/20)x] - x = 420

Simplifying further:

[(33/20) - 1]x = 420

[(33/20) - (20/20)]x = 420

[(13/20)x] = 420

Finally, we can solve for x:

x = (420 * 20) / 13

Using a calculator, we find that x ≈ 646.15.

Therefore, the total number of families in the collective farm is approximately 646.

Please note that the given information does not provide the exact number of families in each village or the total number of families in the collective farm. The calculation above is based on the given proportions and assumptions.